How can vertex paint be rendered?
You should plug your vertex colors into the color input of your shader.


With your object selected, add a new material:





Create a meaningful name for the new material. Next, open a node editor window. One way to do this is to create a new UI window by dragging up the triangle in the bottom-left of an existing widow:




You can change the type of your new window with the button on the bottom-left -- select "Node Editor"




You have to type the name of your vertex color layer into the Attribute node. The default name is Col:




You can check the name of vertex color layer in the Vertex Color section of the Object Data tab in the Properties panel: